Hi Phill,
I assume you installed with the Microsoft Web Application Gallery if you are using a "default" DB. In that case, you are using MSSQL. Your connection string is set in the user.config file, open it up and make sure that it is correct. If you are unsure what your database is named or the user/password combination for the database, you will need to use your host's control panel to find the DB name and the username. As for the password you will have to reset it.
It sounds to me like you uploaded a good copy of the web.config and bad copy the user.config from your computer to your server, overwriting the files that were there. At that point, the site could no longer connect to the database because the user.config didn't have the correct connection information. That is why you were being directed to the Setup page, and when you set the DisableSetup key False, Setup told you that it couldn't connect to the database. At this point you copied the web.config from your server to your local computer and got the error about the system.web.extensions section of the web.config. This error is common with mismatched .NET versions (app is 3.5 but website app pool is 4.0). So you probably have .NET 3.5 setup for the website on your computer and .NET 4 on your server, but I really have no idea for sure at this point. You will need to use your host's control panel to find that information. Keep in mind that if you see .NET 2 set on your site, it is 99% likely that it is really .NET 3.5 because it is just a superset of .NET 2.0 so it identifies as such.
I suggest getting the server installation running properly and once it is, we'll tackle the local computer issue. If you aren't familiar with your host's control panel, you will need to contact them for help with it. If it is WebSitePanel or DotNetPanel, I can help you to a limited extent.
HTH,
Joe D.